Republic of Ireland boss Martin O'Neill is confident assistant Roy Keane would be a good fit for Celtic if they turned to him in the a search for a new manager.
Some bookmakers have suspended betting on the former Manchester United and Ireland skipper, who had a brief spell at Parkhead as his playing career drew to a close, replacing Ronny Deila at the helm.
Keane, 44, spoke to the Bhoys two summers ago about the vacancy to which Deila was eventually appointed, and O'Neill, himself a hugely-successful former Celtic boss, is confident he could do the job.
Speaking as he announced a 35-man squad for Ireland's pre-Euro 2016 finals friendly against Holland on May 27 at a press conference in Dublin on Thursday, he said: "I think Celtic is one of the great clubs in the world and I have to say that he was one of the great players in the world, so that's not a bad fit for a start.
"Could he do the job? I would have no problems with that whatsoever. Would he be capable of doing that? Absolutely. But as Roy said, you still have to be asked and so far, I'm not so sure that that's been the case.
"But I don't think that he would give things up here lightly. Something would have to, as he often says, his favourite phrase, rock his boat - I think is what he says.
"But he has enjoyed it here. I think it has been good for him, but is he ready to go? Yes, he could very well be."
Keane has served as O'Neill's number two since November 2013 and the pair have formed a solid working partnership as they have guided the Republic to this summer's finals in France.
However, the older man has always suspected he would ultimately lose the former Sunderland and Ipswich boss to club football once again and insists he would not stand in his way if the opportunity came along.
Asked if he still expected to be working with Keane when the World Cup qualifiers get under way next season, O'Neill said: "I wouldn't know, really, I certainly wouldn't know that. Anything can happen between now and the start of next season. Who can say?
"But I think I have said to you before, I think Roy will want to go and manage in his own right and make the decisions, which is important. He has been used to making a lot of decisions throughout his life both as a player and a captain, and as a manager.
"I think this has been very, very good for him. Will he want to manage on his own again? Absolutely, and if an opportunity comes up, a really good opportunity, then I would wish him all the best."
O'Neill has had to contend with the limelight Keane attracts throughout their time together, but he remains confident he would continue to prosper without his sidekick.
He said with a smile: "Well, up until a couple of years ago, Roy Keane wasn't really in my life and I survived. I must have asked him for his advice when he was three, but if health allows me, I'm sure I will survive."
In the meantime, the two men will focus on preparing their players for the finals with the game against the Dutch, after which O'Neill will cut down the squad to 23, and a final warm-up fixture against Belarus during their training camp in Cork.
Everton full-back Seamus Coleman, who has been sidelined since the middle of last month by a hamstring problem, is included, as is 35-year-old skipper Robbie Keane, who has returned to action for the LA Galaxy after undergoing knee surgery, while there is a first senior call-up for Oxford midfielder Callum O'Dowda.